## A Fuller Explanation: The Synergetic Geometry of R. Buckminster FullerIn a broad sense Design Science is the grammar of a language of images rather than of words. Modern communication techniques enable us to transmit and reconstitute images without the need of knowing a specific verbal sequential language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multidimensional. Architectural renderings commonly show projections onto three mutually perpendicular planes, or consist of cross sections at differ ent altitudes representing a stack of floor plans. Such renderings make it difficult to imagine buildings containing ramps and other features which disguise the separation between floors; consequently, they limit the creativity of the architect. Analogously, we tend to analyze natural structures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. |

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### Contents

The Irrationality of Pi | 15 |

Systems and Synergy | 25 |

Tools of the Trade | 36 |

12 | 41 |

Eulers Law | 43 |

Intertransformability | 51 |

Structure | 60 |

Frequency and Size | 66 |

In Search of Cosmic Hierarchy | 143 |

Jitterbug | 159 |

A and BQuanta Modules | 189 |

Mite | 195 |

AllSpace Fillers | 203 |

GreatCircle Patterns | 209 |

Energy Paths | 226 |

The Invisible Made Visible | 232 |

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720 degrees adjacent angular array balls Buckminster Fuller Bucky central angle Chapter circles closest packing cluster complete compression concept configuration consists corners create cube cuboctahedron defined degenerate stellation degenerate truncation described dimension dual dual polyhedra edge lengths eight energy events equilateral exactly example experience faces Figure forces four four-valent frequency geodesic dome geometric great-circle hedron hexagons icosahedral icosahedron inherent isotropic vector matrix jitterbug layers Loeb Loeb's mathematics minimum system molecules nature nature's nest number of edges number of vertices observation octahedra octahedron octant Octet Truss omnisymmetrical pairs pattern integrity pentagons physical planar plane polygon polyhedron principles pyramids radial ratio regular polyhedra relationship result rhombic dodecahedron rotational shape of space shell simple space-filling spatial specific sphere-packing spherical stability structure surface angles symmetry Synergetics tensegrity tension tetra three-frequency tion topology triangles triangular truncated octahedron twelve two-frequency unit Universe vector equilibrium vertex volume